Besides what F&S said, Morro Bay State Park is scenic and has some power and water sites and a dump station. A lesser known campground between Morro Bay and SLO on Hwy 1 is El Chorro Regional Park and they have full hookups. Also Morro Strand State Beach which has no hookups and is kind of like a parking lot, but is right on the beach. Pismo State Beach (North Beach) is adjacent to the beach and behind the dunes...large sites, no hookups, dump station, but busy in summer. Port San Luis has first come first served sites right on the bay, very scenic if you can get one. There are also numerous private campgrounds, but those are generally too packed in for my taste.

Regardless, you need to make reservations now especially if staying anywhere on a weekend. Fog in the coastal areas is at it's worst in June and the locals refer to it as June Gloom. There are some county parks that are inland from the coast that are sunnier but can be very hot. These are Lopez Lake and Santa Margarita Lake. There is very little water in the lakes now because of the exceptional drought.